Consider any right-angled triangle with one of the acute angles being θ. We define the trigonometric functions as follows:
Do the values of the trigonometric functions depend on the specific triangle we consider? No. We shall now explain this in detail. Let us recollect the idea of similarity of triangles, which we learnt in high school. If ∆ABC and ∆PQR are such that each angle of ∆ABC is equal to an angle of ∆PQR, then these two triangles are said to be similar. For similar triangles, the three pairs ...